physics 101: lecture 12, pg 1 physics 101: lecture 12 2d collisions and center of mass
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Physics 101: Lecture 12, Pg 1
Physics 101: Physics 101: Lecture 12Lecture 122D2D Collisions and Collisions and
Center of massCenter of mass
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Physics 101: Lecture 12, Pg 2
Example: stopping carExample: stopping carVo=40 m/s
m = 1500 kg
µs = 0.6
How long does it take the car to stop?
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Physics 101: Lecture 12, Pg 3
Momentum is ConservedMomentum is Conserved
Momentum is “Conserved” meaning it can not be created nor destroyed Can be transferred
Total Momentum does not change with time.
This is a BIG deal!
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Physics 101: Lecture 12, Pg 4
Example: collisionExample: collision“before” “after”
M1=2kg M2=3kg M2=3kgM1=2kg
Vo = 5m/sVo = 0m/s
Two blocks collide and stick together, what is their final velocity?
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Physics 101: Lecture 12, Pg 5
Example: collisionExample: collision“before” “after”
M1=2kg M2=3kg M2=3kgM1=2kg
Vo = 5m/sVo = 2m/s
Two blocks collide and stick together, What direction is their final velocity?
A)Right
B)Left
C)The final velocity is zero
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Physics 101: Lecture 12, Pg 6
Example: collisionExample: collision“before” “after”
M1=2kg M2=3kg M2=3kgM1=2kg
Vo = 5m/sVo = 2m/s
Two blocks collide and stick together, what is their final velocity?
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Physics 101: Lecture 12, Pg 7
Example: cannon (explosion)Example: cannon (explosion)
mc = 200kgmb = 5 kg
v = 300 m/s
What is the velocity of the cannon?
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Physics 101: Lecture 12, Pg 8
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Physics 101: Lecture 12, Pg 9
ExplosionsExplosions “before”
“after”
M
m1m2
• Example: m1 = M/3 m2 = 2M/3• Which block has larger |momentum|?
* Each has same |momentum|
• Which block has larger speed?
* mv same for each smaller mass has larger velocity
• Which block has larger kinetic energy?
* KE = mv2/2 = m2v2/2m = p2/2m
* smaller mass has larger KE
• Is mechanical (kinetic) energy conserved?
* NO!!
v1 v2
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A=1, B=2, C=same
0 = p1+p2
p1= -p2
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Physics 101: Lecture 12, Pg 10
Collisions or Explosions in Collisions or Explosions in Two DimensionsTwo Dimensionsy
x
before after
• Ptotal,x and Ptotal,y independently conserved
Ptotal,x,before = Ptotal,x,after
Ptotal,y,before = Ptotal,y,after37
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Physics 101: Lecture 12, Pg 11
before afterppf
vvoo = 3m/s = 3m/s
FF
vvcm
Example: shooting poolExample: shooting pool
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during
Mass of both balls is 2kg
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Find final velocity and direction of white ball
At rest
vvf =2m/s
vvf =2m/s
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Physics 101: Lecture 12, Pg 12
Example: shooting pool (cont.)Example: shooting pool (cont.)
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Physics 101: Lecture 12, Pg 13
Block 1 of mass M1 = 10kg has an initial velocity of 5m/s in the Block 1 of mass M1 = 10kg has an initial velocity of 5m/s in the +x direction. It collides with Block 2 of mass M2 = 5kg which, +x direction. It collides with Block 2 of mass M2 = 5kg which, initially has a velocity of 15m/s in the +y direction. If the two initially has a velocity of 15m/s in the +y direction. If the two
blocks stick together what is the final speed and direction of the blocks stick together what is the final speed and direction of the two blocks?two blocks?
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Physics 101: Lecture 12, Pg 14
H
L LL L
m
M
A projectile of mass m moving horizontally with speed v strikes a stationary mass M suspended by strings of length L. Subsequently, m + M rise to a height of H.
Given H, M and m what is the initial speed v of the projectile?
M + mv
V
V=0
See I.E. 1 in homeworkSee I.E. 1 in homework
Ballistic PendulumBallistic Pendulum
demo 29
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Physics 101: Lecture 12, Pg 15
Ballistic PendulumBallistic Pendulum
Collision Conserves Momentum
After, Conserve Energy
Combine:
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Physics 101: Lecture 12, Pg 16
Center of MassCenter of MassCenter of Mass = Balance point
i
cm m
rmrmr 2211
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Some objects can’t be balanced on a single point
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Physics 101: Lecture 12, Pg 17
Example: center of massExample: center of mass
m = 0.140 kg
1m
0.1m
M =
0.515
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Physics 101: Lecture 12, Pg 18
SummarySummary• Collisions and Explosions
•Draw “before”, “after” •Define system so that Fext = 0
•Set up axes•Compute Ptotal “before”
•Compute Ptotal “after”
•Set them equal to each other
• Center of Mass (Balance Point)
icm m
rmrmr 2211
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